Topological proof of Benoist-Quint's orbit closure theorem for SO(d,1)

Minju Lee; Hee Oh

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arXiv · 1903.02696

Topological proof of Benoist-Quint's orbit closure theorem for SO(d,1)

Minju Lee·Hee Oh

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Abstract

We present a new proof of the following theorem of Benoist-Quint: Let $G:=SO^\circ(d,1)$, $d\ge 2$ and $\Delta<G$ a cocompact lattice. Any orbit of a Zariski dense subgroup $\Gamma$ of $G$ is either finite or dense in $\Delta\backslash G$. While Benoist and Quint's proof is based on the classification of stationary measures, our proof is topological, using ideas from the study of dynamics of unipotent flows on the infinite volume homogeneous space $\Gamma\backslash G$.

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Minju Lee, Hee Oh. 2019-03-07. Topological proof of Benoist-Quint's orbit closure theorem for SO(d,1). https://arxiv.org/abs/1903.02696

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